PKB: a program system and data base for analysis of protein structure

Gibbs sampling and helix-cap motifs

Protein backbones have characteristic secondary structures, including alpha-helices and beta-sheets. Which structure is adopted locally is strongly biased by the local amino acid sequence of the protein. Accurate (probabilistic) mappings from sequence to structure are valuable for both secondary-structure prediction and protein design. For the case of alpha-helix caps, we test whether the information content of the sequence-structure mapping can be self-consistently improved by using a relaxed definition of the structure. We derive helix-cap sequence motifs using database helix assignments for proteins of known structure. These motifs are refined using Gibbs sampling in competition with a null motif. Then Gibbs sampling is repeated, allowing for frameshifts of +/-1 amino acid residue, in order to find sequence motifs of higher total information content. All helix-cap motifs were found to have good generalization capability, as judged by training on a small set of non-redundant proteins and testing on a larger set. For overall prediction purposes, frameshift motifs using all training examples yielded the best results. Frameshift motifs using a fraction of all training examples performed best in terms of true positives among top predictions. However, motifs without frameshifts also performed well, despite a roughly one-third lower total information content.

Crystine: fibrous biomolecular material from protein crystals cross-linked in a specific geometry

Cysteine substitutions were engineered on the surface of maltose binding protein to produce crystine fibers, linear polymers of folded protein formed within a crystal. Disulfide bond formation between adjacent protein molecules within the lattice was monitored by X-ray crystallography. The cross-linked crystals were resistant to dissolution in water or neutral buffer solutions, even though the cross-linking was one-dimensional. However, crystine fibers were observed by transmission electron microscopy to dissociate from the crystals in acidic solutions. Some fibers remained associated as two-dimensional bundles or sheets, with a repeat unit along the fibers consistent with the packing of the individual protein molecules in the crystal. Neutralization of the acidic solutions caused the fibers to re-associate as a solid. Crystine threads were drawn out of this solution. In scanning electron microscopy images, many individual fibers could be seen unwinding from the ends of some threads. Crystine fibers are a new type of biomolecular material with potential applications wherever the use of proteins in a fibrous form is desirable, for example, the incorporation of enzymes into cloth or filtration material.

Extent and nature of contacts between protein molecules in crystal lattices and between subunits of protein oligomers

A survey was compiled of several characteristics of the intersubunit contacts in 58 oligomeric proteins, and of the intermolecular contracts in the lattice for 223 protein crystal structures. The total number of atoms in contact and the secondary structure elements involved are similar in the two types of interfaces. Crystal contact patches are frequently smaller than patches involved in oligomer interfaces. Crystal contacts result from more numerous interactions by polar residues, compared with a tendency toward nonpolar amino acids at oligomer interfaces. Arginine is the only amino acid prominent in both types of interfaces. Potentials of mean force for residue-residue contacts at both crystal and oligomer interfaces were derived from comparison of the number of observed residue-residue interactions with the number expected by mass action. They show that hydrophobic interactions at oligomer interfaces favor aromatic amino acids and methionine over aliphatic amino acids; and that crystal contacts form in such a way as to avoid inclusion of hydrophobic interactions. They also suggest that complex salt bridges with certain amino acid compositions might be important in oligomer formation. For a protein that is recalcitrant to crystallization, substitution of lysine residues with arginine or glutamine is a recommended strategy.

Evaluation of threading specificity and accuracy

Threading experiments with proteins from the globin family provide an indication of the nature of the structural similarity required for successful fold recognition and accurate sequence-structure alignment. Threading scores are found to rise above the noise of false positives whenever roughly 60% of residues from a sequence can be aligned with analogous sites in the structure of a remote homolog. Fold recognition specificity thus appears to be limited by the extent of structural similarity, regardless of the degree of sequence similarity. Threading alignment accuracy is found to depend more critically on the degree of structural similarity. Alignments are accurate, placing the majority of residues exactly as in structural alignment, only when superposition residuals are less than 2.5 A. These criteria for successful recognition and sequence-structure alignment appear to be consistent with the successes and failures of threading methods in blind structure prediction. They also suggest a direct assay for improved threading methods: Potentials and alignment models should be tested for their ability to detect less extensive structural similarities, and to produce accurate alignments when superposition residuals for this conserved "core" fall in the range characteristic of remote homologs.

Threading a database of protein cores

We present an analysis of 10 blind predictions prepared for a recent conference, "Critical Assessment of Techniques for Protein Structure Prediction." The sequences of these proteins are not detectably similar to those of any protein in the structure database then available, but we attempted, by a threading method, to recognize similarity to known domain folds. Four of the 10 proteins, as we subsequently learned, do indeed show significant similarity to then-known structures. For 2 of these proteins the predictions were accurate, in the sense that a similar structure was at or near the top of the list of threading scores, and the threading alignment agreed well with the corresponding structural alignment. For the best predicted model mean alignment error relative to the optimal structural alignment was 2.7 residues, arising entirely from small "register shifts" of strands or helices. In the analysis we attempt to identify factors responsible for these successes and failures. Since our threading method does not use gap penalties, we may readily distinguish between errors arising from our prior definition of the "cores" of known structures and errors arising from inherent limitations in the threading potential. It would appear from the results that successful substructure recognition depends most critically on accurate definition of the "fold" of a database protein. This definition must correctly delineate substructures that are, and are not, likely to be conserved during protein evolution.

Derivation of rules for comparative protein modeling from a database of protein structure alignments

We describe a database of protein structure alignments as well as methods and tools that use this database to improve comparative protein modeling. The current version of the database contains 105 alignments of similar proteins or protein segments. The database comprises 416 entries, 78,495 residues, 1,233 equivalent entry pairs, and 230,396 pairs of equivalent alignment positions. At present, the main application of the database is to improve comparative modeling by satisfaction of spatial restraints implemented in the program MODELLER (Sali A, Blundell TL, 1993, J Mol Biol 234:779-815). To illustrate the usefulness of the database, the restraints on the conformation of a disulfide bridge provided by an equivalent disulfide bridge in a related structure are derived from the alignments; the prediction success of the disulfide dihedral angle classes is increased to approximately 80%, compared to approximately 55% for modeling that relies on the stereochemistry of disulfide bridges alone. The second example of the use of the database is the derivation of the probability density function for comparative modeling of the cis/trans isomerism of the proline residues; the prediction success is increased from 0% to 82.9% for cis-proline and from 93.3% to 96.2% for trans-proline. The database is available via electronic mail.

Knowledge-based model building of proteins: concepts and examples

We describe how to build protein models from structural templates. Methods to identify structural similarities between proteins in cases of significant, moderate to low, or virtually absent sequence similarity are discussed. The detection and evaluation of structural relationships is emphasized as a central aspect of protein modeling, distinct from the more technical aspects of model building. Computational techniques to generate and complement comparative protein models are also reviewed. Two examples, P-selectin and gp39, are presented to illustrate the derivation of protein model structures and their use in experimental studies.

An empirical energy function for threading protein sequence through the folding motif

In this paper we present a new residue contact potential derived by statistical analysis of protein crystal structures. This gives mean hydrophobic and pairwise contact energies as a function of residue type and distance interval. To test the accuracy of this potential we generate model structures by "threading" different sequences through backbone folding motifs found in the structural data base. We find that conformational energies calculated by summing contact potentials show perfect specificity in matching the correct sequences with each globular folding motif in a 161-protein data set. They also identify correct models with the core folding motifs of hemerythrin and immunoglobulin McPC603 V1-domain, among millions of alternatives possible when we align subsequences with alpha-helices and beta-strands, and allow for variation in the lengths of intervening loops. We suggest that contact potentials reflect important constraints on nonbonded interaction in native proteins, and that "threading" may be useful for structure prediction by recognition of folding motif.

Pair distribution functions in small systems: implications for protein structure analysis

A general formula is derived for the relation between the pair correlation function and the histogram of interparticle distances in small nonuniform systems. The formula is applied to random packings of spheres in a spherical container, which are generated by a Monte Carlo method. When measured properly, the resultant correlation functions are very similar to ones in bulk systems with the same volume fraction of particles. In contrast, the density is very nonuniform as a function of distance from the center of the container. The variation is an order of magnitude for the number density of particle centers, or severalfold for the occupied volume fraction. It is described how these results can be used to analyze the forces that determine protein structure.

SESAM: a relational database for structure and sequence of macromolecules

A system is described that provides ways of integrating data on protein structure, sequence, and survey results, with molecular graphics and molecular mechanics software. Its major component is the relational database SESAM, presently implemented under the commercial package SYBASE. By design, the database allows full integration--within the same data organization--of raw data on protein structure, sequence, ligands, and heterogroups, obtained from the Brookhaven Protein Databank, with pure sequence information available from other databanks such as SWISS-PROT. It contains in addition higher level descriptions of structural and topological properties, as well as survey results, obtained by executing specialized computer programs. Aside from the very useful attribute of closely combining structural and nonstructural information, other important features distinguish it from analogous systems developed elsewhere. It includes a molecular dictionary with complete description of geometric properties and energy parameters used in modeling and conformational energy calculations. Using this dictionary, structural data are validated by checking for localized inconsistencies in atomic coordinates, atomic symbols, chirality definitions, and flagging errors and incomplete entries. Because of both the dictionary and the validation procedures, SESAM can be readily interfaced with conventional molecular graphics and mechanics software packages, or with other specialized application programs. With the aid of appropriate interfaces, data access is sufficiently fast for SESAM to be interrogated interactively. Prototypes of user interfaces, as well as an interface with the molecular graphics package BRUGEL, are described and the power of the system is illustrated in applications such as homology-based protein modeling, computer-aided protein design, protein structure predictions, analysis of local structure motifs, and of relationships between protein sequence and structure.

The protein-folding problem: the native fold determines packing, but does packing determine the native fold?

A globular protein adopts its native three-dimensional structure spontaneously under physiological conditions. This structure is specified by a stereochemical code embedded within the amino acid sequence of that protein. Elucidation of this code is a major, unsolved challenge, known as the protein-folding problem. A critical aspect of the code is thought to involve molecular packing. Globular proteins have high packing densities, a consequence of the fact that residue side chains within the molecular interior fit together with an exquisite complementarity, like pieces of a three-dimensional jigsaw puzzle [Richards, F. M. (1977) Annu. Rev. Biophys. Bioeng. 6, 151]. Such packing interactions are widely viewed as the principal determinant of the native structure. To test this view, we analyzed proteins of known structure for the presence of preferred interactions, reasoning that if side-chain complementarity is an important source of structural specificity, then sets of residues that interact favorably should be apparent. Our analysis leads to the surprising conclusion that high packing densities--so characteristic of globular proteins--are readily attainable among clusters of the naturally occurring hydrophobic amino acid residues. It is anticipated that this realization will simplify approaches to the protein-folding problem.

The frequency of ion-pair substructures in proteins is quantitatively related to electrostatic potential: a statistical model for nonbonded interactions

A statistical analysis of ion pairs in protein crystal structures shows that their abundance with respect to uncharged controls is accurately predicted by a Boltzmann-like function of electrostatic potential. It appears that the mechanisms of protein folding and/or evolution combine to produce a "thermal" distribution of local nonbonded interactions, as has been suggested by statistical-mechanical theories. Using this relationship, we develop a maximum likelihood methodology for estimation of apparent energetic parameters from the data base of known structures, and we derive electrostatic potential functions that lead to optimal agreement of observed and predicted ion-pair frequencies. These are similar to potentials of mean force derived from electrostatic theory, but departure from Coulombic behavior is less than has been suggested.